Fluid flow analysis

ABSTRACT

A method of determining a measure of wave speed or wave intensity in a fluid conduit comprises uses ultrasound measurements to determine the conduit diameter, as a function of time, at a longitudinal position of the conduit, and uses ultrasound measurements to determine fluid velocity, as a function of time, in a volume element at said longitudinal position of the conduit. The ultrasound measurement to determine fluid velocity is effected by tracking objects within the fluid flow in successive frames sampling the volume element, and obtaining displacement vectors for the objects. A wave speed may be determined from a ratio of the change in fluid velocity at the longitudinal position as a function of time and the change in a logarithmic function of the conduit diameter as a function of time. A measure of wave intensity may be determined as a function of change in determined conduit diameter and corresponding change in fluid velocity.

The present invention relates to methods and apparatus for usingultrasound to analyse fluid flow in fluid conduits. In particularly,though not exclusively, the invention applies to such methods andapparatus useful for analysing fluid flows in human or animalcirculatory systems.

When the heart contracts during each heartbeat, it increases thepressure and speed of the blood in the arteries immediately connected toit. This disturbance propagates as a wave down the arterial system. Aneveryday example of this phenomenon is that the pulse can be felt in thewrist. The wave travels at a speed or velocity that depends on thestiffness of the arteries, and reflections of the wave occur at anypoint where the vessel geometry or wall properties change. The velocityof the waves and the intensity of the initial wave and its reflectionstherefore contain information about the performance of the heart and thestate of the vessels. It is therefore useful to measure these propertiesto provide a useful means for diagnosing cardiovascular disease andthose at risk from it.

Pulse waves in arteries can therefore be used for assessing (a) theperformance of the heart, since it generates the waves, (b) arterialstiffness, which determines the velocity of the waves, and (c) changesin arterial or peripheral vessel cross section or mechanical properties,which reflect the waves. Wave phenomena can readily be assessed frominvasive, catheter-based measurements and are increasingly used for thefunctional assessment of coronary artery stenosis. Their use in otherareas of cardiovascular medicine has been impeded by the difficulty ofmaking accurate, non-invasive measurements.

It is an object of the invention to provide a method and apparatus foranalysis of fluid flows in fluid conduits such as arteries which canpreferably be implemented non-invasively. In one aspect, the inventionseeks to provide an ultrasound-based system for assessing wave phenomenathat is non-invasive and suitable for the clinical investigation ofheart failure, arterial stiffening, altered vascular tone andendothelial dysfunction, for example.

According to one aspect, the invention provides a method of determininga measure of wave speed in a fluid flowing through a fluid conduit, themethod comprising:

-   -   using ultrasound measurements to determine the conduit diameter        or conduit cross-sectional area, as a function of time, at a        longitudinal position of the conduit;    -   using ultrasound measurements to determine fluid velocity, as a        function of time, in a volume element at said longitudinal        position of the conduit, the ultrasound measurement to determine        fluid velocity being effected by tracking objects within the        fluid flow in successive frames sampling the volume element, and        obtaining displacement vectors for the objects;

determining a wave speed from a function of (i) the change in fluidvelocity at the longitudinal position as a function of time and (ii) thechange in the conduit diameter as a function of time.

The wave speed may be determined from a ratio of the change in fluidvelocity at the longitudinal position as a function of time and thechange in a logarithmic function of the conduit diameter as a functionof time. The wave speed may be determined from a ratio of a change influid velocity at the longitudinal position within a time interval and acorresponding change in a logarithmic function of the conduit diameterwithin the same time interval. The wave speed may be determined from thechange in fluid velocity at the longitudinal position within a timeinterval and a corresponding change in the conduit diameter within thesame time interval. The fluid velocity may be determined using imagingvelocimetry. The ultrasound measurements for determining fluid velocitymay comprise a series of B-mode images or B-mode RF data. Obtainingdisplacement vectors may comprise correlating the locations of thetracked objects in successive frames of the B-mode images or B-mode RFdata. The ultrasound measurements for determining conduit diameter andfluid velocity may be both derived from a common ultrasound transducerhead. The common transducer head may be directed orthogonally to thefluid flow axis of the fluid flow conduit. The ultrasound measurementsfor determining conduit diameter and fluid velocity may be both derivedfrom common ultrasound excitation and response signals. The ultrasoundmeasurements for determining conduit cross-sectional area and fluidvelocity may be both derived from common ultrasound excitation andresponse signals. The wave speed, c, may be determined according to theequation c=0.5 (dU/dInD), where dU is a change in the fluid velocity asa function of time and dInU is a change in the natural logarithm of D asa function of time. The fluid conduit may comprise a part of the humanor animal circulatory system. The method may include repeating theultrasound measurements and determining a wave speed at multiple timesduring a cardiac cycle and correlating the measurement of wave speedwith time within the cardiac cycle. The method objects being tracked maycomprise red blood cells, white blood cells, platelets or contrast agententities. The method may include determining a measure of fluid conduitwall elasticity or distensibility at the volume element, from the wavespeed. The wave speed, c, may be determined according to the equationc=AdU/dA or c=dU/dInA, where A is the cross-sectional area, dA is thechange in cross-sectional area as a function of time, dU is the changein the fluid velocity, and dInA is the change in the natural logarithmof A as a function of time.

According to another aspect, the invention provides a method ofdetermining a measure of wave speed in a fluid flowing through a fluidconduit, the method comprising:

-   -   using ultrasound measurements to determine the conduit diameter,        as a function of time, at a longitudinal position of the        conduit;    -   using ultrasound measurements to determine fluid velocity, as a        function of time, in a volume element at said longitudinal        position of the conduit, the ultrasound measurement to determine        fluid velocity being effected by tracking objects within the        fluid flow in successive frames sampling the volume element, and        obtaining displacement vectors for the objects;    -   determining a change in flow rate through the conduit based on        the fluid velocity measurements and the conduit diameter        measurements;    -   determining a change in cross-sectional area of the conduit        based on the conduit diameter measurements; and    -   determining a wave speed from a ratio of the change in flow rate        at the longitudinal position as a function of time and the        change in conduit cross-sectional area as a function of time.

The fluid velocity may be determined using imaging velocimetry. Theultrasound measurements for determining fluid velocity may comprise aseries of B-mode images or B-mode RF data. Obtaining displacementvectors may comprise correlating the locations of the tracked objects insuccessive frames of the B-mode images or B-mode RF data. The ultrasoundmeasurements for determining conduit diameter and fluid velocity may beboth derived from a common ultrasound transducer head. The commontransducer head may be directed orthogonally to the fluid flow axis ofthe fluid flow conduit. The ultrasound measurements for determiningconduit diameter and fluid velocity may be both derived from commonultrasound excitation and response signals. The wave speed, c, isdetermined according to the equation c=dQ/dA), where dQ is a change inthe fluid flow rate and dA is a change in the cross-sectional area ofthe conduit. The fluid conduit may comprise a part of the human oranimal circulatory system. The method may include repeating theultrasound measurements and determining a wave speed at multiple timesduring a cardiac cycle and correlating the measurement of wave speedwith time within the cardiac cycle. The objects being tracked maycomprise red blood cells, white blood cells, platelets or contrast agententities. The method may include determining a measure of fluid conduitwall elasticity or distensibility at the volume element, from the wavespeed.

A method of determining a measure of wave intensity in a fluid conduit,the method comprising:

-   -   using ultrasound measurements to determine the conduit diameter,        as a function of time, at a longitudinal position of the        conduit;    -   using ultrasound measurements to determine fluid velocity, as a        function of time, in a volume element at said longitudinal        position of the conduit, the ultrasound measurement to determine        fluid velocity being effected by tracking objects within the        fluid flow in successive frames sampling the volume element, to        obtain displacement vectors for the objects;    -   determining a measure of wave intensity as a function of change        in determined conduit diameter and corresponding change in fluid        velocity.

The fluid velocity may be determined using imaging velocimetry. Theultrasound measurements for determining fluid velocity may comprise aseries of B-mode images or B-mode RF data, and obtaining displacementvectors comprises correlating the locations of the tracked objects insuccessive frames of the B-mode images or B-mode RF data. The ultrasoundmeasurements for determining conduit diameter and fluid velocity may beboth derived from a common ultrasound transducer head. The commontransducer head may be directed orthogonally to the fluid flow axis ofthe fluid flow conduit. The ultrasound measurements for determiningconduit diameter and fluid velocity may be both derived from commonultrasound excitation and response signals. The method may includedetermining a wave speed in the fluid conduit. The measure of waveintensity may be determined as a function of the determined conduitdiameter, the determined fluid velocity and the determined wave speed.The measure of wave intensity may be determined according to theequation:

${dI}_{\pm} = {\frac{1}{4\left( {D\text{/}2c} \right)}\left( {{dD} \pm {\frac{D}{2c}{dU}}} \right)^{2}}$

where dI+ is the forward wave intensity, dI− is the backward waveintensity; D is the conduit diameter; dD is the change in the conduitdiameter; c is the wave speed; dU is the change in fluid velocity. Themeasure of wave intensity is determined according to the equationdI=dDdU, where dI is the wave intensity; dD is the change of conduitdiameter; and dU is the change of fluid velocity. The method may includedetermining wave energy by integrating the wave intensity over a periodof time. The wave speed may be determined as a function of a ratio ofthe change in fluid velocity at the longitudinal position as a functionof time and the change in a logarithmic function of the conduit diameteras a function of time. The wave speed, c, may be determined according tothe equation c=0.5(dU/dInD), where dU is a change in the fluid velocityas a function of time and dInU is a change of the natural logarithm of Das a function of time. The fluid conduit may comprise a part of thehuman or animal circulatory system. The method may include repeating theultrasound measurements and determining a wave intensity at multipletimes during a cardiac cycle and correlating the measurement of waveintensity with time within the cardiac cycle. The objects being trackedmay comprise red blood cells, white blood cells, platelets or contrastagent entities. The method may include determining a measure of fluidconduit cross-sectional properties upstream and or downstream of thesampled volume element from the wave intensity. The method may includedetermining a cardiac output profile from the wave intensity.

According to another aspect, the invention provides an apparatus fordetermining a measure of wave speed in a fluid conduit, comprising ananalysis module configured to perform the steps of any of the methods ofdetermining wave speed as described above.

According to another aspect, the invention provides an apparatus fordetermining a measure of wave intensity in a fluid conduit, comprisingan analysis module configured to perform the steps of any of the methodsof determining wave intensity as described above.

Embodiments of the present invention will now be described by way ofexample and with reference to the accompanying drawings in which:

FIG. 1 is a schematic diagram of a fluid conduit and ultrasoundtransducer in cross-section useful in explaining a fluid flow analysistechnique;

FIG. 2 is a schematic functional block diagram of an ultrasound fluidflow analysis system;

FIG. 3 shows results of fluid velocity measurements in an artery (FIGS.3a and 3b ) and conduit diameter measurement (FIG. 3c );

FIG. 4 shows results of measured wave intensities in a rabbit centralear artery.

ARTERIAL PULSE WAVES AND THEIR RELATION TO CLINICALLY IMPORTANTCARDIOVASCULAR PROPERTIES a) Wave Fundamentals

Pulse waves originate from the heart and travel forwards from theproximal (upstream) end of the arterial system towards the periphery.Reflections originate more peripherally, at sites where vascularproperties change; the reflected waves travel backwards, and can thenre-reflect forwards and backwards between reflection sites until theydissipate. Pushing more blood into the artery gives a compression wavewhereas suction gives a decompression wave. A compression wave willincrease pressure and accelerate flow if it originates proximal to themeasurement site, whilst a decompression wave will decrease pressure andretard flow. Methods described in this disclosure may generally relateto measuring the speed and/or intensity and/or reflection of suchcompression/decompression waves travelling through a fluid flowing in afluid conduit such as the circulatory system. The waves may generally beconsidered to comprise disturbances in fluid pressure, fluid velocityand fluid conduit diameter that propagate along the fluid conduit withtime. In preferred arrangements exemplified herein, the fluid is bloodand the fluid conduits comprise blood vessels and components of thecirculatory system.

b) Waves and Cardiac Performance

The left ventricle generates forward-going waves in non-coronarysystemic arteries. A compression wave arises at the start of systolebecause the contraction of the ventricle causes the pressure and flow ofblood to increase. A forward expansion wave that arises in late systoleis thought to be generated by momentum, which carries the blood forwardas ventricular contraction slows and then relaxes, resulting in adecrease in pressure and flow. These waves are altered inclinically-important conditions. For example, the left ventricleproduces a smaller compression wave in patients with systolic heartfailure, including dilated cardiomyopathy [1, 2], whereas hypertrophiccardiomyopathy causes diastolic dysfunction and results in a lesspowerful expansion wave [2].

c) Local Arterial Compliance

The speed, c, of wave travel in arteries is conventionally termed PulseWave Velocity (PWV). It is related to the distensibility of the wall andthe density of blood by the Bramwell Hill equation

c ²=1/(density×distensibility).

Hence PWV is a measure of arterial stiffness: the stiffer the artery,the faster the wave speed. Peripheral arteries have a higher PWV thancentral ones, and arteries stiffen with age [3]. PWV is clinicallyimportant because it is a strong, independent cardiovascular risk factor[4], and because arteries stiffen when they become diseased [5].

Elasticity of a blood vessel can be obtained from wave speed (or PWV) bythe Moens-Korteweg equation:

c ²=(E _(inc) h)/(2r rho)

where E_(inc) is the incremental elastic modulus, h is the vessel wallthickness, r is the vessel radius, and rho (ρ) is blood density.

A stretchy artery has low elastic modulus and high distensibility, sofor the same vessel (i.e. for the same h and r), they are reciprocallyrelated:

Distensibility=(2r)/(h E _(inc)).

d) Wave Reflections

Pulse waves are reflected at vascular sites where there is a change incross-sectional area or wave speed. Changes in area occur at sites ofbranching or taper, and changes in wave speed occur where wall structurealters. Wave reflections are clinically important; the ASCOT trial, forexample, showed increased reflection to be a strong independentpredictor of cardiovascular events in hypertensives [6]. Wavereflections can account for the different left ventricular masses inpatients taking different anti-hypertensive medication, despite similarbrachial blood pressures [7], and they maintain systolic blood pressurein patients with heart failure [1].

Measurement of Arterial Pulse Wave Characteristics

PWV has been assessed by transit time methods. In an invasivetransit-time technique, a catheter having two pressure sensors a knowndistance apart is inserted into an artery, and the time delay betweenthe arrival of the pressure wave at the two sites is used in conjunctionwith their separation to find the wave speed. Non-invasive assessment ofPWV using this principle is also possible. Detection can be based onpressure measured by applanation tonometry, velocity measured usingDoppler ultrasound, or volume measured by photoplethysmography. It isalso possible to make measurements with MRI [9,10] but this may be toocostly for routine use. Sites are much further apart than with theinvasive technique: typically, transit times between the carotid andfemoral arteries are assessed.

The catheter-based method is considered too invasive for routine use inpeople. Unfortunately, the non-invasive methods also suffer fromlimitations. First, it is difficult to obtain an accurate value for thepath-length from the heart to each of the measuring sites, especially inpatients with obesity or tortuous vessels. Second, the methods give aPWV averaged over several vessels, rather than local values. That is animportant issue because different arteries stiffen with age at differentrates [3] and have different relations to disease [10,11]; localmeasurements should have much greater clinical value (although sincethey are less widely used, there have been few attempts to validatetheir predictive value). Third, femoral waveforms may be difficult torecord accurately or may be modified in patients with a range of medicalconditions. Fourth, and most importantly, all these methods assess thevelocity of the waves but not their intensity or reflection.

Attempts have been made to overcome these issues by developing methodsfor obtaining PWV at a single site. That eliminates the problemsassociated with averaging PWV over large arterial distances and obviatesthe need for estimating those distances. Additionally, the measurementsrequired for determining PWV at a single site generally also make itpossible to analyse wave intensities and reflections, as explainedbelow. Theoretically, then, such techniques could be of great value.

In these single-site methods, wave properties are determined bycontinuously and simultaneously measuring both blood pressure (P) andblood velocity (U). PWV can be derived from the ratio of the change in P(dP) to the change in U (dU) between successive measurements, if P and Uare measured during phases of the cardiac cycle when forward wavesdominate [12]. Further characterisation of the waves was revolutionisedby the Wave Intensity Analysis (WIA) methods developed over the last 20years by Parker and co-workers [13]; an on-line tutorial is given at[14]. Their mathematical derivation is complex but the equations derivedfor their practical application are straightforward. The wave intensity,dI, at any time in the cardiac cycle is obtained from the product of dPand dU. Knowing PWV (see above) additionally allows the wave to bedecomposed into forward and backward components.

P and U can be measured invasively with catheter-based arterial probes.This method has been used in many WIA studies, for example where WIA isused to determine the severity of coronary stenosis [15]. However, theinvasive nature of the technique is highly restrictive. Attempts havetherefore been made to develop non-invasive alternatives.

In locations where arteries overlie hard structures and are relativelyclose to the body surface, P can be measured by applanation tonometryand U by Doppler ultrasound [1]. Utility is limited by the number ofvessels that can be accessed in this way, as well as by the need tocalibrate the tonometer data. (Peak systolic pressures vary betweenarteries due to different patterns of wave reflection; hence, pressuresshould be assessed by sphygmomanometry of the brachial artery to obtainabsolute mean and diastolic pressures—these are constant throughout thearterial system and can therefore be used to calibrate tonometricmeasurements from the vessel of interest. Alternatively, pressures couldbe assessed by tonometry that has been calibrated by sphygmomanometry ofthe same vessel.) Most importantly, it is impossible to apply bothprobes to the same site at the same time; this means that the P and Udata streams have to be acquired separately, ensemble averaged and thentime aligned by the ECG, introducing significant errors.

Another non-invasive method [2] has been implemented which uses acombination of Doppler and M-Mode ultrasound to measure U and arterialdiameter D, respectively. A linear relation between the diameter of theartery and the pressure inside it is assumed, in order to obtain the Prequired for conventional WIA. The use of Doppler and M-Mode can beproblematic since these modes require different beam angles, making itdifficult to image the same arterial segment. Furthermore, thecalibration of the pressure-diameter relationship is complex, as justdescribed for tonometry. (In practice this is so involved that it israrely done, and carotid diameters are incorrectly calibrated by simplebrachial sphygmomanometry.) Finally, the assumption that P and D areproportional is fundamentally incorrect since arteries have non-linearstress-strain curves. Beulen et al [16] have suggested methods toovercome this last issue by non-linearly estimating P from D, but theseinvolve a long chain of assumptions and have not been tested underphysiological conditions. Another technique combining Doppler withB-mode or M-mode ultrasound is given in [55].

The invention overcomes the limitations of existing systems because itobviates the need for measuring P (invasively) or estimating it(inaccurately) from measurements of diameter, D.

An alternative form of WIA is based directly on U and D, rather than Uand P [17]. PWV can be obtained from the ratio of the change in U to thesimultaneous change in the natural logarithm of D (preferably, at apoint in the cycle when forward waves dominate):

c=0.5(dU/dInD).

Wave intensity is given by:

${dI}_{\pm} = {\frac{1}{4\left( {D\text{/}2c} \right)}\left( {{dD} \pm {\frac{D}{2c}{dU}}} \right)^{2}}$

where dI+ is the forward wave intensity, dI− is the backward waveintensity; D is the conduit diameter; dD is the change of the conduitdiameter; c is the wave velocity; dU is the change of fluid velocity.

This analysis technique has been validated in silicon model systems [18](including a geometrically and mechanically accurate model of the humanaorta and its major branches [19]) and with data acquired in humanaortas by Dr Wilkinson and colleagues (Cambridge), using MRI [20].

Ultrasound may be used to obtain the D and U data required by this newanalysis technique, thereby avoiding the use of costly MRI. Conventionalultrasound B-mode methods can be used to determine D. To avoid theproblem of different beam angle requirements inherent in Doppler andM-mode measurements (discussed above), in a new technique describedherein, Doppler ultrasound is not used to determine U. Instead, a formof particle image velocimetry known as ultrasound image velocimetry(UIV) is used. In this method, a series of B-mode images, or theradio-frequency (RF) data from which they derive, is acquired andregional cross correlation is performed on sequential images todetermine the local displacement of the ultrasound scatterers. Theultrasound scatterers may be any suitable objects, such as red bloodcells, white blood cells, platelets or microbubble contrast agents,which can be tracked through consecutive image frames. From thesedisplacements, and the acquisition frame rate, a full 2-D velocity fieldis found. Combining the axial velocities obtained by this method withthe new WIA equations means that for the first time, wave velocities,intensities and reflections can be obtained non-invasively, withoutunreliable conversion of D to P, from data streams obtainedsimultaneously at the same location.

With reference to FIG. 1, a fluid conduit 1 has a longitudinal axis 2which may be referred to as the z-axis and conveys a fluid 3therethrough with a dominant flow direction 4 generally along thez-axis. In an example, the fluid conduit 1 may be a vessel in the humanor animal circulatory system. An ultrasound transducer 10 is positionedto direct ultrasonic excitation energy along a beam axis 11 which istransverse to the fluid conduit longitudinal axis 2, and preferably isorthogonal to the fluid conduit longitudinal axis 2, i.e. the beam axis11 is on the y-axis as shown, the x-axis being into the plane of thedrawing. The transducer preferably comprises an array of transducerelements.

The ultrasound transducer 10 generates an excitation beam 12 comprisingexcitation signals configured to sample a longitudinal position orextent 13 of the conduit 1 along the z-axis and a lateral extent alongthe x-axis. The transducer 10 receives response signals, from which aregenerated a succession of image frames. At least a part of each imageframe represents a volume element 15. The volume element 15 represents afinite segment of the conduit along the z-axis, and may represent aportion of the conduit in x- and y-space (orthogonal to the dominantflow axis) or may represent a full slice through the conduit, i.e. thefull conduit width in one or both of x and y. In a basic configuration,UIV is performed on the volume element which is a full slice through theconduit diameter and the stated finite segment of the conduit along thez-axis, and variation in wave velocity across the conduit diameter isnot considered.

Each image frame provides a spatial map of ultrasound-scattering objectsin the flow and correlation of successive image frames enables thevelocity of selected objects passing through the volume element 15 to bedetermined, in accordance with established ultrasound imagingvelocimetry techniques. The objects may, for example, be red bloodcells, white blood cells or platelets in blood flow through an artery inthe human or animal circulatory system. The objects may, for example, bemicrobubble contrast agents within the blood flow. More generally, theobjects may be any objects such as single particles or clumps ofparticles capable of being distinguished in the ultrasound images fromreceived ultrasound echo signals. In one arrangement, identifiableobjects in the first image of the volume element 15 are identified in asuccessive, e.g. second, image of the volume element to see how far theobjects have travelled. The objects may be speckles or speckle patterns.The identification of the objects in the second image may be performedusing an autocorrelation method. The autocorrelation method may beapplied to groups of objects.

The ultrasound transducer 10 may also be configured to transmitultrasound excitation signals to the conduit 1 and to receivecorresponding ultrasound response signals indicative of the positions 16of the conduit walls. Successive measurements are used to determinechanges in diameter D of the conduit 1 at the longitudinal position 13,which measurements are correlated in time with corresponding objectvelocity measurements.

The transducer 10 effecting the velocity measurements and the transducereffecting the conduit wall positions 16 may comprise the same transducerhead.

The fluid flowing in the conduit 1 is subject to pressure waves such asthose caused by the heart pumping action, arterial elasticity andarterial topology as discussed earlier. The wave velocity of suchpressure waves may be determined according to the expressionc=0.5(dU/dInD), where dU is a change in the fluid velocity as a functionof time and dInD is a change in the natural logarithm of D as a functionof time. The expression “as a function of time” is intended to encompassany changes determined by successive measurements of the relevantproperty at known time intervals such as unit time intervals (e.g. theultrasound imaging frame rate) or variable time intervals, or at timeswhen two different properties being measured can be correlated to acommon point in time or time interval, as well as an instantaneousmeasurement of the first time derivative of that property. In apreferred arrangement, D and U are determined periodically according tothe frame rate of the ultrasound transducer 10. In another arrangement,dU/dt and dInD/dt may be used to determine wave speed or velocity.

The change in fluid velocity within the volume element 15 may bedetermined by measuring the fluid velocity at two or more successivetimes, e.g. using the ultrasound imaging velocimetry technique. Thechange in the logarithmic function of D may be determined by measuringthe diameter from the ultrasound response signals at the same two ormore successive times.

Wave velocity c can then be determined by direct computation of theratio of these two changes. Alternatively, the rate of change of fluidvelocity, dU/dt, may be determined for a sample period and the rate ofchange of the logarithmic function of conduit diameter, dInD/dt, may bedetermined for a corresponding, but not necessarily identical, sampleperiod. The sample periods are preferably coextensive or overlapping orcontiguous, but in any event are sufficiently close in time thatmeasured changes in fluid velocity are correlated in time with measuredchanges in conduit diameter.

In general aspect, the measured fluid velocity U may be that of a singleobject or group of objects as discussed above, or may be aggregated overa plurality of objects within the volume element. In this respect, thefluid velocity may be expressed as an average fluid velocity for thevolume element 15. As stated earlier, the volume element can comprise afull cross-section of the conduit diameter and the average fluidvelocity can therefore be the mean velocity across the conduit diameter.

The ultrasound response signals used to derive both fluid velocity andconduit diameter may comprise B-mode image data. The B-mode image datamay comprise RF data from which B-mode images may be derived, and thefluid velocity may be determined directly from the RF data. The B-modeimage data may comprise B-mode images. The ultrasound response signalsused to derive both fluid velocity and conduit diameter may be obtainedas responses to common ultrasound excitation signals. The ultrasoundresponse signals used to derive both fluid velocity and conduit diametermay comprise B-mode data. The conduit diameter may be obtained withfewer transducer elements than required for a B-mode image, even down toa single transducer element used more frequently, e.g. M-mode. Thiscould be interleaved with the full B-mode imaging used to obtain thevelocity. Use of the M-mode could give a more accurate measure of thediameter as a function of time.

For measurements made in a human or animal circulatory system, the fluidvelocity and conduit diameters may be determined at multiple timesduring each cardiac cycle. The determination of wave velocity may thenbe determined at multiple times during each cardiac cycle and/or thewave velocity may be determined only at selected times during eachcardiac cycle. The wave velocity may be determined at a point in thecardiac cycle when forward waves dominate at the longitudinal position13.

From the measurements of wave velocity, a measure of the fluid conduitwall elasticity, at the longitudinal position 13 of the volume element15, may be made.

In an alternative arrangement, the wave velocity may be computedaccording to a slightly different methodology. The ultrasound data usedto determine the conduit diameter D, as a function of time, at thelongitudinal position 13 of the conduit 1 may be used to calculate across-sectional area A of the conduit as a function of time. Theultrasound measurements used to determine fluid velocity as a functionof time, in the volume element 15 at the longitudinal position 13 of theconduit 1, may be used to calculate a total flow rate Q through theconduit as a function of time. Again, the expression “as a function oftime” is intended to encompass any changes determined by successivemeasurements of the relevant property (e.g. Q or A) at known timeintervals such as unit time intervals or variable time intervals, or attimes when two different properties being measured can be correlated toa common point in time or time interval, as well as an instantaneousmeasurement of the first time derivative of that property. In apreferred arrangement, Q and A are determined periodically according tothe frame rate of the ultrasound transducer 10. The measurements Q and Acan be determined from velocity measurements U and diameter measurementsD by assuming radial symmetry. Alternatively, with some more recent 3Dultrasound systems, it may be possible to obtain Q and A directly.

The wave velocity c may then be determined according to a ratio of achange in flow rate and a corresponding change in cross-sectional areaof the conduit, e.g. c=dQ/dA. Change in flow rate through the conduitmay be based on successive fluid velocity measurements and conduitdiameter measurements. Change in cross-sectional area of the conduit maybe based on successive conduit diameter measurements.

The wave velocity c can also therefore be determined according to aratio of a change in fluid velocity and a corresponding change incross-sectional area of the conduit, e.g. using a relationship asoutlined in [52],

c=AdU/dA=dU/dInA,

where A is the cross-sectional area, dA is the change in cross-sectionalarea, and dU is the change in flow velocity. It can be understood thatif changes in area are negligible compared to changes in velocity, thenthe c=dQ/dA expression [53] would be equivalent to c=AdU/dA. Otherwisethey are only approximately the same.

Since A, and changes in A, can be determined according to the ultrasoundmeasurements of D, this can be seen as a function of changes in conduitdiameter. Thus, in a general aspect, wave speed can be determined from afunction of (i) the change in fluid velocity at the longitudinalposition as a function of time and (ii) the change in the conduitdiameter as a function of time, or wave speed can be determined from aratio of the change in flow rate at the longitudinal position as afunction of time and the change in conduit cross-sectional area as afunction of time. It will be understood that in this context, a measureof the change in cross-sectional area in a conduit having a circularcross-section can readily be obtained from the measure of change incross-sectional diameter. It will also be understood that for a conduitwith, e.g. a non-circular cross-section, multiple measurements ofdiameter (at different angles about the conduit longitudinal axis) ormultiple chord measurements (which may or may not include a “diameter”in the strict mathematical sense of a line passing through the centre ofthe conduit) may be used to determine cross-sectional area and therebyto determine changes in cross-sectional area.

A measure of wave intensity can also be calculated from the ultrasoundmeasurements as described above, and in particular from the determinedconduit diameter and fluid velocity. A measure of wave intensity may bedetermined according to the equation:

${dI}_{\pm} = {\frac{1}{4\left( {D\text{/}2c} \right)}\left( {{dD} \pm {\frac{D}{2c}{dU}}} \right)^{2}}$

where dI+ is the forward wave intensity, dI− is the backward waveintensity; D is the conduit diameter; dD is the change in the conduitdiameter; c is the wave speed; dU is the corresponding change in fluidvelocity.

A measure of wave intensity can also be determined according to theequation dI=dDdU, where dI is the wave intensity; dD is the change ofconduit diameter; and dU is the corresponding change of fluid velocity.

A measure of wave energy, I, can also be determined by integrating thewave intensity dI over a period of time. The period of time may be fromthe start of a wave to the end of a wave and/or over a predeterminedportion of a cardiac cycle. Determining wave energy I may be useful forlong lasting waves of low intensity.

From the measure of wave intensity at longitudinal position 13, it ispossible to determine a measure of performance of the heart. It is alsopossible to determine a measure of fluid conduit wall stiffness andcross-sectional properties at the longitudinal position and also bothupstream and downstream of the longitudinal position 13 by suitableanalysis over the cardiac cycle, for example by analysis of reflections,particularly by calculating the intensity of reflected waves, thereflection coefficients and the distance to reflection sites. Thecross-sectional properties may include properties such as wallstiffness, wall thickness, vessel cross-sectional area, branching,bifurcation, pathological alteration of wall properties, etc.

With reference to FIG. 2, an exemplary apparatus for determining wavevelocity and wave intensity and wave energy is described.

Ultrasound transducer 10 is coupled to an ultrasound system module 20.An excitation module 21 or driver provides signals 22 to the transducer10 to generate ultrasound excitation signals for insonification of thefluid conduit 1, particularly adapted to generate response signals froma selected volume element 15 at a longitudinal position 13 of the fluidconduit 1 as seen in FIG. 1. Response signals 23 from the transducer 10are passed to an ultrasound imaging velocimetry (UIV) analysis module 24and to a geometric structure analysis module 25. The UIV analysis module24 is configured to determine a succession of fluid velocitymeasurements, i.e. to determine fluid velocity as a function of time,using UIV techniques as described above. The UIV analysis module 24 mayalso or instead be configured to calculate the total flow rate Q throughthe conduit as a function of time, also as discussed above. Thegeometric structure analysis module 25 is configured to determine asuccession of conduit diameter measurements, i.e. to determine conduitdiameter as a function of time, derived from ultrasound response signalsfrom the conduit walls, using techniques as described above. Thegeometric structure analysis module 25 may also be configured todetermine a succession of cross-sectional area measurements of theconduit from the successive diameter measurements.

The measurements of fluid velocity as a function of time and conduitdiameter as a function of time are passed to wave velocity analysismodule 26 and/or wave intensity analysis module 27.

Wave velocity analysis module 26 is configured to determine wavevelocity either (i) from a ratio of the change in fluid velocity and thecorresponding change in logarithmic function of conduit diameter, or(ii) from a ratio of the change in flow rate and the change in conduitcross-sectional area, at the longitudinal position 13 of the conduit,using techniques as described above.

Wave intensity analysis module 27 is configured to determine waveintensity as a function of change in conduit diameter and correspondingchange in fluid velocity, using techniques as described above.

EXAMPLES

In a preferred arrangement, improved UIV methods such as those describedin [21-24] may be used. These were implemented on an Ultrasonix scannerand showed that, although the data were noisy, they give blood flowvelocities comparable to theoretical predictions and to invasivemeasurements in vitro, and that they non-invasively give velocitymeasurements comparable to those obtained by Doppler ultrasound in arabbit aorta in vivo as shown in FIG. 3. FIG. 3a shows flow velocitydata from UIV analysis in the rabbit aorta. Velocity measurements areindicated by the magnitudes of arrows 30 for a plurality of spatiallocations along the conduit flow axis (z) and transverse to the conduitflow axis (x). These represent a velocity vector field overlaid on anultrasound B-mode image. Any one or more of these velocity measurements30 may be used to derive the velocity in a volume element 15 of FIG. 1.A succession of such velocity measurements 30 over time, which may beaveraged over the conduit cross-section, may be used to derive fluidvelocity as a function of time, as discussed above, and thereby changein velocity. A set of the velocity measurements 30 through across-section of the fluid conduit (e.g. all measurements 30 along across-sectional (x) axis may be used to determine a flow rate throughthe conduit. FIG. 3b shows maximum measured velocity from a Dopplerspectrum (line 31) from a Doppler ultrasound technique compared tomaximum velocity as measured by the UIV technique (line 32). FIG. 3cshows a measurement of conduit diameter (aorta diameter) measured fromthe B-mode images using a simple intensity peak method.

From the UIV data, diameters obtained from the same scans, and the newapproach described herein, we calculated a wave speed of 3.6 m/s, whichis well within the accepted range of values.

Ultrafast ultrasound imaging systems have recently been developed formedical applications [25]. They beam-form and acquire data from alltransducer elements in parallel instead of line by line, giving a framerate up to two orders of magnitude higher than conventional scanners.The technique is likely to form the basis of the next generation ofclinical scanners. For our purposes, the massively increased frame rateenables more accurate tracking of the rapid changes in flow and diameterthat occur in arteries, and it also reduces signal-to-noise ratios byallowing averaging of repeat measurements even while meeting thestringent temporal resolution requirements. We have implemented UIV onthe new system and validated it in straight tubes, arterial phantoms andin the rabbit aorta by comparison against analytical solutions andDoppler measurements [26]; data quality was vastly improved by thehigher frame rate [26].

The ultrasound system module 20 of FIG. 2 may be further adapted toinclude a real-time graphical user interface 28 that shows a currentB-mode image and a preliminary estimate of velocity from UIV, allowing auser to select a region for analysis.

The system module 20 may further include a semi-automated echo trackingmethod for monitoring arterial diameter. The position of the luminalsurface of upper and lower conduit walls may first be marked manually,e.g. using interface 28. A cross correlation of the RF signals may thenbe used to track their position and hence obtain changes in conduitdiameter D.

Imaging and UIV variables such as plane wave steering angles and UIVtracking window sizes may be optimised for accuracy and precision. RFdata filtering may be incorporated to optimise the ultrasound signalsfor UIV measurements.

A recently-described factor [27] that corrects PWV for effects of wavereflections may be incorporated into the control software of the systemmodule 20.

All data from the system may be transmitted to a database 29 for furtherprocessing. Wave velocity and/or wave intensity analysis modules 26, 27may be provided as separate apparatus, e.g. for off-line processing andcalculation of wave speed, intensity and reflection from data capturedto the database 29.

The system 20 may be used to detect circulatory abnormalities in humansand animals by monitoring changes in wave intensities, which are alteredin heart failure patients, using the non-invasive techniques described.

Assessment of endothelial function: it has been noted that thevasodilator nitric oxide (NO) changes the height of the dichrotic notch(a point of inflection between the systolic and diastolic peaks) in thepressure or volume wave. Substances which stimulate NO release, such asacetylcholine (ACh), lower the height of the dichrotic notch. Substanceslike L-NAME that inhibit NO production raise the height of the dichroticnotch, relative to the overall amplitude of the wave. It has been shownthat these changes are quite specific to NO (and the relatednitrovasodilators); they do not reflect general influences of vasoactiveagents on peripheral tone, blood pressure or heart rate. The effect maybe due to altered wave reflections as illustrated in FIG. 4. The system20 may be deployed to determine the effects of NO on wave reflections.

In FIG. 4, wave intensities in a rabbit central ear artery are shown.FIG. 4a illustrates wave intensity as a function of time for a baselinecondition; FIG. 4b illustrates wave intensity as a function of timeafter administration of ACh; and FIG. 4c illustrates wave intensity as afunction of time after administration of L-NAME. The initial wave(forward compression) has been truncated to more clearly show itsreflection from the lower body (line 41, second wave). In FIG. 4b ,which illustrates the maximum NO condition, this is a single peak 43. Itdevelops a shoulder 44 in the baseline state (less NO) and a double peak45 with L-NAME (least NO), indicating that NO is altering thesereflections.

The system 20 may be usable to detect heart failure, age-relatedarterial stiffening and NO-dependent wave reflection in pre-clinicalmodels.

Traditional methods for analysing pulse waves are based on Fourieranalysis. The results are in the frequency domain, which makes it hardto relate them to any feature of clinical relevance. Wave IntensityAnalysis, in contrast, conceptualises waves as being built up ofinfinitesimal wavefronts that travel forward or backwards with knownintensities at specific times. The breakdown of the pulse wave in thisway makes it much easier to relate its features to real cardiac andvascular properties.

WIA may be used in procedures that evaluate the functional significanceof coronary stenoses, and hence determine whether intervention isrequired. It identifies naturally wave-free periods during the cardiaccycle. At such points, the ratio of pressure upstream and downstream ofa stenosis can be used to assess the resistance it causes. In aconventional procedure, such periods are not identified and waves mayhave to be eliminated by administering vasodilating drugs, which is timeconsuming, expensive, unpleasant for the patient and not feasible insome patient groups. The techniques described herein may provide anon-invasive method without requiring catheterization.

The system may be used for investigating Heart Failure. Curtiss et al[1] compared normal subjects and patients with compensated systolicheart failure. The energy in a re-reflected expansion wave (the X wave)was 80% lower in the patients. Interestingly, the augmentation indexbased on tonometry—a supposed measure of wave reflections that is notbased on WIA—was unchanged. Takaya et al [37] examined patients havingchronic heart failure with normal ejection fraction under exercisetesting, an accepted method for predicting survival. No transthoracicechocardiography parameters correlated significantly with any exerciseparameter, but the intensity of the forward expansion wave (W2)correlated significantly with all exercise parameters, implying thatthis simple non-invasive measure will better predict outcome. Vriz et al[38] conducted a longitudinal study of patients with heart failure andreduced ejection fraction, comparing wave parameters withechocardiographic indices of left ventricular function. Averagefollow-up was >3 yr. On stepwise backward multiple regression, only awave parameter—the intensity of W2—was an independent predictor ofoutcome. Li and Guo [39] assessed the value of WIA in differentiatingnon-obstructive hypertrophic cardiomyopathy (NOHCM) from leftventricular hypertrophy secondary to hypertension (LVHSH). They examinedthe forward going compression (W1) and expansion (W2) waves and an areaof negative wave intensity (NA) resulting from peripheral reflections.W2 was lower in NOHCM than in LVHSH and in normal subjects. NA washigher in LVHSH than in NOHCM and normal subjects. The wave intensityparameters differed to a much greater extent than the transthoracic echoparameters: W2 differed 3-fold and NA nearly 2-fold between NOHCM andLVHSH groups, whereas the largest TTE changes were about 40%. Thus WIAis likely to be useful for differentiating between different types ofheart failure. Siniawski et al [40] examined patients suffering fromend-stage dilative cardiomyopathy and awaiting transplant. Univariatelogistic regression analysis was performed to assess the predictivevalue of WIA, VO2max, invasively assessed pressures and stroke volume,and echocardiographically-measured ejection fraction. The strongestpredictor of events was the 1st peak of wave intensity. Indeed it wasonly on the basis of the wave parameters that the two groups could bedistinguished, again suggesting WIA will predict outcomes.

The clinical need for measuring arterial stiffness, or PWV as asurrogate, is well known—it has frequently been reviewed, and is thesubject of consensus or policy documents from expert groups [41,42]. Thedifficulties and disadvantages of estimating global PWV are presentedabove. There is much interest in assessing local wall stiffness forclinical purposes and many manufacturers have consequently devisednon-invasive methods for doing so. These methods are based onechotracking—they use ultrasound to measure the change in arterialdiameter over the cardiac cycle. In order to obtain wall stiffness, itis also necessary to know the local systolic and diastolic pressures.Unfortunately, this brings us back to the problems discussed forapplanation tonometry, above. In the method described herein, bycontrast, local PWV is obtained from measurements of U and D—pressuresare not required—and measurements are feasible from all vessels that canbe imaged by ultrasound (including substantial segments of the aorta).

The methods described herein may be used to diagnose endothelialdysfunction through its influence on wave reflections. Endothelialdysfunction—characterised principally by a reduction in NObioavailability—is a strong risk factor for cardiovascular disease butrarely assessed. That is unfortunate because a number of lifestylechanges have been shown to improve endothelial function. Severalpharmacological approaches are also under investigation [43, 44]. It islikely to reflect the technical challenge of measuring such dysfunction.The only method approaching acceptance, at least in a research context,involves inducing flow mediated dilatation: an occlusive cuff is placedaround the forearm, inflated above systolic pressure for severalminutes, and then released. The increased flow resulting from reactivehyperaemia increases haemodynamic shear stress on the brachial arteryendothelium, leading to NO release and dilatation of the vessel. Theincrease in diameter is assessed from ultrasound images [45]. Althoughthis measure is related to cardiovascular risk [46], many technicalissues remain: methods of normalisation for baseline diameter introduceartefacts [47]; cuff position, duration of occlusion and timing ofmeasurement seem critical, and with some the dependence on NO isquestionable [48]; there is individual variation in the degree ofreactive hyperaemia but normalising by the shear stress appears to causeadditional problems [49]; and there is great operator dependence thatneeds to be minimised by holding the probe with a micrometer-adjustablestereotaxic apparatus [48]. In the methods described herein, endothelialfunction could be assessed from the effect of NO on pulse waves ratherthan solely on diameter.

Current ultrafast ultrasound systems can resolve down to 100 microns,which is more than adequate for obtaining sufficient accuracy in the dDterm and the resolution in velocity is <1% of peak velocity and leads toacceptably small errors in dU. Furthermore, the speed of such system(>1000 frames/s) is sufficient to “freeze” the motion of vessels thatmove during the cardiac cycle. To date, signal-to-noise ratios have beenacceptable and microbubble contrast agents could be used to improve themfurther, for example by distinguishing non-linear signals emitted by themicrobubbles and linear signals emitted by the tissue.

The methods of determining wave speed and/or determining wave intensitygenerally have application in any non-rigid fluid conduit system,particularly within a system exhibiting elastic behaviour in the wallsin at least part of the system. The expression ‘conduit’ encompassespipes and tubes which may have varying diameters and cross-sectionalprofiles, which may be branching and which may have chambers connectedthereto. Generally, the techniques described could be applied in anyelastic walled fluid conduit which has sufficient transparency toultrasound to enable the tracking of objects within a flow of fluidwithin the conduit. The techniques could generally be applicable to asystem where compression/decompression waves may arise within the fluidconduit, e.g. from the operation of valves within the system.

The equations used as described above, to determine wave speed, waveintensity, and/or wave energy, can be modified for greater accuracy totake into account other measurable properties of the system such asviscosity of the fluid medium (e.g. blood), viscoelasticity of theconduit walls and other non-linear effects. In one method [57], this maybe achieved by making additional measurements of D or U (or equivalentlyadditional measurements of A or Q) at a second site along the conduit.The equations used to determine wave speed could be modified to takeaccount of reflections, e.g. using a correction factor as derived by PSegers et al [27].

Wave intensity analysis techniques such as those used in this disclosurecan be improved by subtracting “windkessel” effects, i.e. subtractingthe pressure that is caused by the elastic vessels being pumped full ofblood, and not by waves [56].

Other Methods for Calculation of Wave Speed

Using pressure and velocity, wave speed is conventionally calculated as

c=(1/rho)(dP/dU)

where rho (φ is fluid density. This method and those exemplified earlierin this document may be used in early systole, when reflections can beconsidered to be negligible.

Wave speed can also be calculated when waves are not unidirectionalusing the “sum-of-squares” method [54]:

c=(1/rho)[(ΣdP ²)/(ΣdU ²)]^(0.5)

where Σ is the sum over the cardiac cycle.

It may be possible to convert this to an equation based on A(cross-sectional area) and D (conduit diameter), such as

c=0.5[(ΣdU ²)/ΣdInD ²)]^(0.5)

thereby also falling within the general ambit of a function of (i) thechange in fluid velocity at the longitudinal position as a function oftime and (ii) the change in the conduit diameter as a function of time.

Other embodiments are intentionally within the scope of the accompanyingclaims.

LIST OF REFERENCES

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1. A method of determining a measure of wave speed in a fluid flowingthrough a fluid conduit, the method comprising: using ultrasoundmeasurements to determine the conduit diameter or conduitcross-sectional area, as a function of time, at a longitudinal positionof the conduit; using ultrasound measurements to determine fluidvelocity, as a function of time, in a volume element at saidlongitudinal position of the conduit, the ultrasound measurement todetermine fluid velocity being effected by tracking objects within thefluid flow in successive frames sampling the volume element, andobtaining displacement vectors for the objects; determining a wave speedfrom a function of (i) the change in fluid velocity at the longitudinalposition as a function of time and (ii) the change in the conduitdiameter or conduit cross-sectional area, as a function of time.
 2. Themethod of claim 1 in which the wave speed is determined from a ratio ofthe change in fluid velocity at the longitudinal position as a functionof time and the change in a logarithmic function of the conduit diameteras a function of time.
 3. The method of claim 2 in which the wave speedis determined from a ratio of a change in fluid velocity at thelongitudinal position within a time interval and a corresponding changein a logarithmic function of the conduit diameter within the same timeinterval.
 4. The method of claim 1 in which the wave speed is determinedfrom the change in fluid velocity at the longitudinal position within atime interval and a corresponding change in the conduit diameter withinthe same time interval.
 5. The method of claim 1 in which the fluidvelocity is determined using imaging velocimetry.
 6. The method of claim1 in which the ultrasound measurements for determining fluid velocitycomprise a series of B-mode images or B-mode RF data, and obtainingdisplacement vectors comprises correlating the locations of the trackedobjects in successive frames of the B-mode images or B-mode RF data. 7.The method of claim 1 in which the ultrasound measurements fordetermining conduit diameter and fluid velocity are both derived from acommon ultrasound transducer head.
 8. The method of claim 7 in which thecommon transducer head is directed orthogonally to a fluid flow axis ofthe fluid flow conduit.
 9. The method of claim 7 in which the ultrasoundmeasurements for determining conduit diameter or conduit cross-sectionalarea, and fluid velocity are both derived from common ultrasoundexcitation and response signals.
 10. The method of claim 1 in which thewave speed, c, is determined according to the equation c=0.5(dU/dInD),where dU is a change in the fluid velocity as a function of time anddInD is a change in the natural logarithm of D as a function of time.11. The method of claim 1 in which the fluid conduit comprises a part ofthe human or animal circulatory system.
 12. The method of claim 11further including repeating the ultrasound measurements and determininga wave speed at multiple times during a cardiac cycle and correlatingthe measurement of wave speed with time within the cardiac cycle. 13.The method of claim 11 in which the objects being tracked comprise redblood cells, white blood cells, platelets or contrast agent entities.14. The method of claim 1 further including determining a measure offluid conduit wall elasticity or distensibility at the volume element,from the wave speed.
 15. The method of claim 1 in which the wave speed,c, is determined according to the equation c=AdU/dA or c=dU/dInA, whereA is the cross-sectional area, dA is the change in cross-sectional areaas a function of time, dU is the change in the fluid velocity as afunction of time, and dInA is the change in the natural logarithm of Aas a function of time.
 16. A method of determining a measure of wavespeed in a fluid flowing through a fluid conduit, the method comprising:using ultrasound measurements to determine the conduit diameter, as afunction of time, at a longitudinal position of the conduit; usingultrasound measurements to determine fluid velocity, as a function oftime, in a volume element at said longitudinal position of the conduit,the ultrasound measurement to determine fluid velocity being effected bytracking objects within the fluid flow in successive frames sampling thevolume element, and obtaining displacement vectors for the objects;determining a change in flow rate through the conduit based on the fluidvelocity measurements and the conduit diameter measurements; determininga change in cross-sectional area of the conduit based on the conduitdiameter measurements; and determining a wave speed from a ratio of thechange in flow rate at the longitudinal position as a function of timeand the change in conduit cross-sectional area as a function of time.17. The method of claim 16 in which the fluid velocity is determinedusing imaging velocimetry.
 18. The method of claim 16 in which theultrasound measurements for determining fluid velocity comprise a seriesof B-mode images or B-mode RF data, and obtaining displacement vectorscomprises correlating the locations of the tracked objects in successiveframes of the B-mode images or B-mode RF data.
 19. The method of claim16 in which the ultrasound measurements for determining conduit diameterand fluid velocity are both derived from a common ultrasound transducerhead.
 20. The method of claim 19 in which the common transducer head isdirected orthogonally to the fluid flow axis of the fluid flow conduit.21. The method of claim 20 in which the ultrasound measurements fordetermining conduit diameter and fluid velocity are both derived fromcommon ultrasound excitation and response signals.
 22. The method ofclaim 16 in which the wave speed, c, is determined according to theequation c=dQ/dA), where dQ is a change in the fluid flow rate and dA isa change in the cross-sectional area of the conduit.
 23. The method ofclaim 16 in which the fluid conduit comprises a part of the human oranimal circulatory system.
 24. The method of claim 23 further includingrepeating the ultrasound measurements and determining a wave speed atmultiple times during a cardiac cycle and correlating the measurement ofwave speed with time within the cardiac cycle.
 25. The method of claim23 in which the objects being tracked comprise red blood cells, whiteblood cells, platelets or contrast agent entities.
 26. The method ofclaim 16 further including determining a measure of fluid conduit wallelasticity or distensibility at the volume element, from the wave speed.27. A method of determining a measure of wave intensity in a fluidconduit, the method comprising: using ultrasound measurements todetermine the conduit diameter, as a function of time, at a longitudinalposition of the conduit; using ultrasound measurements to determinefluid velocity, as a function of time, in a volume element at saidlongitudinal position of the conduit, the ultrasound measurement todetermine fluid velocity being effected by tracking objects within thefluid flow in successive frames sampling the volume element, to obtaindisplacement vectors for the objects; determining a measure of waveintensity as a function of change in determined conduit diameter andcorresponding change in fluid velocity.
 28. The method of claim 27 inwhich the fluid velocity is determined using imaging velocimetry. 29.The method of claim 27 in which the ultrasound measurements fordetermining fluid velocity comprise a series of B-mode images or B-modeRF data, and obtaining displacement vectors comprises correlating thelocations of the tracked objects in successive frames of the B-modeimages or B-mode RF data.
 30. The method of claim 27 in which theultrasound measurements for determining conduit diameter and fluidvelocity are both derived from a common ultrasound transducer head. 31.The method of claim 30 in which the common transducer head is directedorthogonally to the fluid flow axis of the fluid flow conduit.
 32. Themethod of claim 30 in which the ultrasound measurements for determiningconduit diameter and fluid velocity are both derived from commonultrasound excitation and response signals.
 33. The method of claim 27further including determining a wave speed in the fluid conduit, and inwhich the measure of wave intensity is determined as a function of thedetermined conduit diameter, the determined fluid velocity and thedetermined wave speed.
 34. The method of claim 27 in which the measureof wave intensity is determined according to the equation:${dI}_{\pm} = {\frac{1}{4\left( {D\text{/}2c} \right)}\left( {{dD} \pm {\frac{D}{2c}{dU}}} \right)^{2}}$where dI+ is the forward wave intensity, dI− is the backward waveintensity; D is the conduit diameter; dD is the change in the conduitdiameter; c is the wave speed; dU is the change in fluid velocity. 35.The method of claim 27 in which the measure of wave intensity isdetermined according to the equation dI=dDdU, where dI is the waveintensity; dD is the change of conduit diameter; and dU is the change offluid velocity.
 36. The method of claim 34 or 35 further includingdetermining wave energy by integrating the wave intensity over a periodof time.
 37. The method of claim 33 in which the wave speed isdetermined as a function of a ratio of the change in fluid velocity atthe longitudinal position as a function of time and the change in alogarithmic function of the conduit diameter as a function of time. 38.The method of claim 37 in which the wave speed, c, is determinedaccording to the equation c=0.5(dU/dInD), where dU is a change in thefluid velocity as a function of time and dInU is a change of the naturallogarithm of D as a function of time.
 39. The method of claim 27 inwhich the fluid conduit comprises a part of the human or animalcirculatory system.
 40. The method of claim 39 further includingrepeating the ultrasound measurements and determining a wave intensityat multiple times during a cardiac cycle and correlating the measurementof wave intensity with time within the cardiac cycle.
 41. The method ofclaim 38 in which the objects being tracked comprise red blood cells,white blood cells, platelets or contrast agent entities.
 42. The methodof claim 27 further including determining a measure of fluid conduitcross-sectional properties upstream and or downstream of the sampledvolume element from the wave intensity.
 43. The method of claim 39further including determining a cardiac output profile from the waveintensity.
 44. Apparatus for determining a measure of wave speed in afluid conduit, comprising: an analysis module configured to perform thesteps of any of claims 1 to
 26. 45. Apparatus for determining a measureof wave intensity in a fluid conduit, comprising: an analysis moduleconfigured to perform the steps of any of claims 27 to 43.